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ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.

ABSTRACT: Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.

SUBMITTER: Hasenauer J

PROVIDER: S-EPMC4081021 | biostudies-literature | 2014 Jul

REPOSITORIES: biostudies-literature

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Project description:BackgroundSeveral new programming languages and technologies have emerged in the past few decades in order to ease the task of modelling complex systems. Modelling the dynamics of complex systems requires various levels of abstractions and reductive measures in representing the underlying behaviour. This also often requires making a trade-off between how realistic a model should be in order to address the scientific questions of interest and the computational tractability of the model.MethodsIn this paper, we propose a novel programming paradigm, called temporal constrained objects, which facilitates a principled approach to modelling complex dynamical systems. Temporal constrained objects are an extension of constrained objects with a focus on the analysis and prediction of the dynamic behaviour of a system. The structural aspects of a neuronal system are represented using objects, as in object-oriented languages, while the dynamic behaviour of neurons and synapses are modelled using declarative temporal constraints. Computation in this paradigm is a process of constraint satisfaction within a time-based simulation.ResultsWe identified the feasibility and practicality in automatically mapping different kinds of neuron and synapse models to the constraints of temporal constrained objects. Simple neuronal networks were modelled by composing circuit components, implicitly satisfying the internal constraints of each component and interface constraints of the composition. Simulations show that temporal constrained objects provide significant conciseness in the formulation of these models. The underlying computational engine employed here automatically finds the solutions to the problems stated, reducing the code for modelling and simulation control. All examples reported in this paper have been programmed and successfully tested using the prototype language called TCOB. The code along with the programming environment are available at http://github.com/compneuro/TCOB_Neuron.DiscussionTemporal constrained objects provide powerful capabilities for modelling the structural and dynamic aspects of neural systems. Capabilities of the constraint programming paradigm, such as declarative specification, the ability to express partial information and non-directionality, and capabilities of the object-oriented paradigm especially aggregation and inheritance, make this paradigm the right candidate for complex systems and computational modelling studies. With the advent of multi-core parallel computer architectures and techniques or parallel constraint-solving, the paradigm of temporal constrained objects lends itself to highly efficient execution which is necessary for modelling and simulation of large brain circuits.

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ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.

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